def find_eliminating_set(G):
'''
a function to find a stable set that eliminates all triangles
Parameters:
G: the graph g to check (networkx)
Returns:
eliminating_set: the set of vertices (list)
'''
cycles = cycle_basis(G)
for v in G.nodes():
cycles += cycle_basis(G, root=v)
triangles = []
for cycle in cycles:
if len(cycle) == 3 and qsort(cycle) not in triangles:
triangles.append(qsort(cycle))
elimintating_set = find_eliminating_set_aux(G, triangles, [])
return elimintating_set
def triangle_free(G):
'''
a function that checks if a graph G is triangle free
Parameters:
G: the graph to check (networkx)
Returns:
condition: True triangle free, False otherwise (boolean)
'''
cycles = cycle_basis(G, root=0)
condition = True
i = 0
while condition and i < len(cycles):
if len(cycles[i]) ==3:
condition = False
i += 1
return condition
